Answer:
Solution: (6, -4)
One solution.
Step-by-step explanation:
In order to graph the given systems of linear equations, a good starting point is plotting the y-intercepts of each equation, and using the slope (rise over run) to plot other points on the graph.
y = -1/6x - 3 ⇒ slope = -1/6 (down 1, run 6), y-intercept (0, -3)
y = -x + 2 ⇒ slope = -1, y-intercept (0, 2)
Attached is a screenshot where it shows the plotted y-intercepts and other points. It shows that the two lines intersect at point (6, -4). We must test to see whether the solution will satisfy both equations in the system:
y = -1/6x - 3
-4 = -1/6(6) - 3
-4 = - 1 - 3
-4 = -4 (True statement).
y = -x + 2
-4 = -6 + 2
-4 = -4 (True statement).
Therefore (6, -4) is the solution that satisfies both equations in the given systems of linear equations.
